The invention relates to a method and apparatus for simulating a physical property of a technical structure, such as motor or a motor part, by automatically generating a mesh of a component model, based on finite elements, and to a corresponding computer program product.
The finite element method (FEM) is a widespread computation method in engineering. As depicted in FIG. 2, in the finite element method, a computational domain 101 is divided into a large number of small, but many, finite elements 102. On the basis of these elements trial functions are usually defined that produce a large system of equations by way of a partial differential equation and the boundary conditions. Then the sought for results are derived from the solved system of equations.
German patent document DE 10360150 A1 discloses a method for generating the envelope of a body based on a predetermined mesh of a construction model in order to reproduce physical events on the surface of a technical system through a finite element simulation.
German patent document DE 10326228 A1, on the other hand, discloses a method for accelerating the meshing for finite element simulations of a system with multiple bodies; and U.S. Pat. No. 6,044,210 discloses a method for determining a finite element model for a structural element.
With standard software for finite element simulations, like ABAQUS, it is already possible to automatically mesh a component model (that is, to describe it by means of a plurality of finite elements). In particular, it is already possible with this standard software to adapt FE (finite element) networks to an example of application. For example, ABAQUS provides a so-called “adaptive remeshing,” which describes in a first step a component model by means of a coarse FE network (synonymous with “coarse mesh of finite elements” or “coarse mesh with finite elements”). Then this network is automatically refined in an area where high mechanical stresses occur, in order to describe in a more suitable manner the component model for additional calculations. The automatic refinement is triggered as a function of the stress gradients between two FE elements. In this procedure the stress gradient between the FE elements is determined, and if it exceeds a certain value, then the network is refined at this point. As a result of the finer resolution, the stress gradient decreases.
This procedure is executed in an iterative manner until the stress gradients satisfy the established criteria. The finer the mesh, the better the mesh can usually describe the component model, the more memory space said model usually requires, and the more computationally intensive the additional calculations or simulations, which are based on this mesh, usually are.
One object of the present invention is to provide a method for simulating a physical property of a technical structure (such as acoustic response) by automatically generating a mesh of a component model, which requires little memory space and yet suitably describes (that is, closely accords with reality) the component model. In this context, the component model may be, for example, a computer accessible construction model of any technical system or any technical structure, like a motor or a motor element or a part of a motor element.
This and other objects and advantages are achieved by the method and apparatus according to the invention, which departs from the prior art technique of proceeding from a coarse mesh, in a step-by-step manner, to a finer mesh. Instead, the technique of the present invention is precisely the reverse: to describe the component model 101 initially by means of a fine mesh (FIG. 2), and then taking this fine mesh as a basis, to pass, in particular, step by step, at least area by area, to a coarser mesh 103. (See FIG. 3.)
This strategy has the advantage that a decision about which area of a component model ought to be finely meshed and which area ought to be coarsely meshed is based on a fine mesh, so that it is more reliable or leads more directly to the target than in the prior art. This approach results in a more adaptive mesh of a component model than in the prior art. Yet it can also make do with little memory space, especially because of the specifically selected areas of the coarse mesh. An additional advantage lies in the fact that an automatic mesh is quite possible, especially if the element size is small.
The present invention is based on the additional idea of pinpointing suitable areas of the component model for description by means of a coarser mesh, by analyzing the deformation behavior of the finite elements.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of one or more preferred embodiments when considered in conjunction with the accompanying drawing.